The first incident happened outside the Royal Bank of Scotland on Church Street at around 9.45am on Tuesday when two men on a Suzuki motorbike pulled up outside as a security worker was entering the building with a cash box.
One of the duo attempted to steal the cash box but was unsuccessful and stole a bag before the men fled on the motorbike towards the direction of Park Square roundabout.
Then, at around 10.30am, detectives believe the same two men stole a cash box from a delivery driver outside a post office on Stradbroke Drive, Sheffield.
Detectives have now released CCTV footage of two men they would like to speak to in connection with the incident.
Kris Thorpiie, who saw the first robbery at the RBS branch, said he was first alerted to the incident after hearing a motorbike ‘revving’.
He said one of the men went into the bank and grabbed a bag before getting back on the motorbike and the men fled down High Street.
Det Sgt Wayne Price said: “Thankfully, no one was injured in either of these incidents and no weapons were used.
“Both of these incidents occurred in busy areas and no doubt there were people who saw what happened or who saw the motorbike pictured prior to the incidents occurring, or just after.”
The RBS was closed for around five hours following the incident and customers were advised to use the Natwest branch on High Street.
It fully reopened at around 2.30pm.
Det Sgt Price added: “We’d like to hear from anyone with information. Did you see what happened? If you can help, please call 101 quoting incident number 996 of January 29.
“You can also speak to Crimestoppers, anonymously, on 0800 555111.”